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10月9日（周五）下午3：00-4：00

：腾讯会议 ID：422470476

New bounds of star-discrepancy for stratified random sampling and applications

要：In this talk, we firstly show an explicit probabilistic star discrepancy bound with Borel measure for N random sampling points. Beck's result are improved and generalized by our results. Then we apply it to estimate the multivariate integration approximation error on a Borel subset of the d-dimensional unit cube $[0,1]^{d}$, and obtain an explicit error bound in the sense of probability. Secondly, we use the strategy of “stratified sampling”to achieve an improved bound for the star-discrepancy of a random point sets with Lebesgue measure, which is of order $O(N^{-\frac{1}{2}-\frac{1}{2d}})$ with probability at least q. Aistleitner and Hofer's result on star discrepancy bound is of order $O(N^{-\frac{1}{2}})$.  Thirdly, we generalize our results to the weighted star-discrepancy and obtain an uniform probabilistic estimates on the multivariate integration approximation error in Sobolev space. Hinrichs, Pillichshammer and Schmid's results are improved. Lastly, we also give some numerical testes to verify our results.

介：中山大学数学学院副院长、教授，博士生导师、国家优秀青年基金获得者，入选广东省“千百十”人才工程培养计划。主要研究方向为应用调和分析、采样理论及其在信号处理中的应用。2004年至今访问过美国耶鲁大学、美国中佛罗里达大学、加拿大Alberta大学，德国亚琛工业大学、法国马赛大学、新加坡国立大学、香港城市大学等高校，相关论文发表在Applied and Computational Harmonic Analysis, Journal of  Fourier analysis and application, BMC bioinformatics, Signal Processing, Proceedings of the American Mathematical society, Journal of Approximation theory等国内外核心期刊。

2020年10月7日

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